He committed adultery and his conscience is troubling him, and he wants to get rid of the foetus

I a Moslem single person, who lives in the USA. I committed adultery many times with the same woman. Now, the women is pregnant. I would like to know if I can marry her in order to solve the problem (I mean cover the scandal)so the baby will find a father and gets the name. Actually, unfortunately, I would prefer abortion and I wish to convince her to do that, but don't know if this is considered killing a person. If so, I would feel guilty because of that. I believe the embryo is about 6-8 weeks. Please I need your help as soon as possible, Jazak Allah Khair.

Praise be to Allaah.
Firstly, my brother in Islam, I offer you my condolences for the faith that you lost during the times when you were committing adultery. For the Prophet (peace and blessings of Allaah be upon him) said: “When an adulterer commits illegal sexual intercourse, then he is not a believer at the time he is doing it, and when a drinker of an alcoholic liquor drinks it, then he is not a believer at the time of drinking it, and when a thief steals, then he is not a believer at the time of stealing, and when a robber robs, and the people look at him, then he is not a believer at the time of doing robbery.” (Narrated by al-Bukhaari, no. 2475) 
Have you not read what your Lord says in His Book? 
“And come not near to unlawful sex. Verily, it is a Faahishah (i.e. anything that transgresses its limits: a great sin, and an evil way that leads one to Hell unless Allaah forgives him)”
[al-Israa’ 17:32 – interpretation of the meaning] 
Do you not know that Allaah sees you wherever you are, and He hears you when you speak? 
Do you not remember the great blessings that Allaah has bestowed upon you? For He is the One Who heals you when you are sick, the One Who feeds you when you are hungry and gives you to drink when you are thirsty. And He has given you the greatest blessing that He has bestowed upon mankind, the blessing of Islam. “Is there any reward for good – other than good?” [al-Rahmaan 55:60 – interpretation of the meaning] 
My brother, ask yourself, Whose dominion do you live under? Whose provision do you eat from? By Whose command do you live? Is it not the dominion of Allaah, the provision of Allaah, the command of Allaah? So how can you disobey Allaah? 
Perhaps you have forgotten the hadeeth of the Mi’raaj, in which the Prophet (peace and blessings of Allaah be upon him) said:
“… then we proceeded and came to something like a tannoor (a kind of oven).” [The narrator] said: “I think he said, ‘in which there were clamouring voices.’” He [the Prophet (peace and blessings of Allaah be upon him)] said: “We looked into it and there we saw naked men and women. Flames were coming to them from the bottom of it, and when the flames reached them, they made an uproar. I said to them [i.e., the two angels who were accompanying him], ‘Who are these?’ They said, ‘Proceed, proceed!’… I said to them, ‘I have seen strange things this night. What is this that I have seen?’ They said, ‘We will tell you…. The naked men and women in the structure that resembled a tannoor oven are the adulterers and adulteresses.’”
(Narrated by al-Bukhaari in Baab Ithm al-Zunaat, no. 7047). 
So you must hasten to repent sincerely before death overtakes you, for the gate of repentance is open until the sun rises from the west or before the soul reaches the throat [at death]. Allaah rejoices over the repentance of His slave, and He will change his bad deeds (sayi’aat) into good deeds (hasanaat). Allaah says (interpretation of the meaning): 
“And those who invoke not any other ilaah (god) along with Allaah, nor kill such person as Allaah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment.
The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;
Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allaah will change their sins into good deeds, and Allaah is Oft Forgiving, Most Merciful.
And whosoever repents and does righteous good deeds; then verily, he repents towards Allaah with true repentance[al-Furqaan 25:68-71] 
Secondly, with regard to your question, “Do I have to marry her?”, this is the issue of the adulterer marrying the woman with whom he committed adultery. The answer is that it is not permissible for him (the adulterer) to marry her, or for her to marry him, until the label of adultery no longer applies to them. That label can only be removed through repentance. 
It is not permissible for you to marry her even if she is Jewish or Christian, because she is a zaaniyah (adulteress). Even if she is Muslim, it is not permissible for you to marry her because she is a zaaniyah.  And it is not permissible for her to accept you as a husband because you are a zaani (adulterer). Allaah says (interpretation of the meaning): 
“The adulterer — fornicator marries not but an adulteress — fornicatress or a Mushrikah; and the adulteress –fornicatress, none marries her except an adulterer — fornicator or a Mushrik [and that means that the man who agrees to marry (have a sexual relation with) a Mushrikah (female polytheist, pagan or idolatress) or a prostitute, then surely, he is either an adulterer — fornicator, or a Mushrik (polytheist, pagan or idolater). And the woman who agrees to marry (have a sexual relation with) a Mushrik (polytheist, pagan or idolater) or an adulterer — fornicator, then she is either a prostitute or a Mushrikah (female polytheist, pagan, or idolatress)]. Such a thing is forbidden to the believers (of Islamic Monotheism)”[al-Noor 24:3] 
The phrase “Such a thing is forbidden to the believers” indicates that this marriage is forbidden. 
“It is essential that both of you repent to Allaah, give up this sin, regret the evil actions that have occurred in the past, resolve not to return to them, and do many righteous deeds, so that Allaah may accept your repentance and turn your bad deeds (sayi’aat) into good deeds (hasanaat). Allaah says (interpretation of the meaning): 
‘And those who invoke not any other ilaah (god) along with Allaah, nor kill such person as Allaah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment.
The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;
Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allaah will change their sins into good deeds, and Allaah is Oft Forgiving, Most Merciful.
And whosoever repents and does righteous good deeds; then verily, he repents towards Allaah with true repentance’
[al-Furqaan 25:68-71] 
If you want to marry her, you have to be sure that she is not pregnant by waiting to see if she menstruates before you do so. If it becomes apparent that she is pregnant, it is not permissible for you to marry her until after she delivers the baby, in accordance with the hadeeth of the Prophet (peace and blessings of Allaah be upon him), in which he forbade a man to use his water to irrigate the crops of another.” 
(Fatwas of the Standing Committee in al-Buhooth al-Islamiyyah magazine, vol. 9, p. 72) 
Thirdly, you say, “so the baby will find a father and gets the name” This is the matter of attributing the child of adultery: who is he to be named after? 
The answer is that the majority of scholars said that the child of adultery should not be named after the adulterer, because the Prophet (peace and blessings of Allaah be upon him) said: “The child goes to the owner of the bed and the adulterer gets nothing but the stones (despair, i.e., to be stoned to death).” (Agreed upon. Al-Bukhaari 2053; Muslim, 1457. Al-Mughni by Ibn Qudaamah, vol. 7, p. 129) 
Fourthly, you say, that you would prefer the woman to get rid of the baby. This is the issue of abortion, and the ruling on that is as stated in the report of the Committee of Senior Scholars (Hay’at Kibaar al-‘Ulamaa’), no. 140, dated 20/6/1407 AH, which is as follows: 
“1 – It is not permissible to abort the pregnancy at any of its various stages except for a legitimate shar’i reason, and within very narrow limits.
2 – If the pregnancy is in the first stage, which is forty days, and aborting it will serve a legitimate shar’i interest or ward off some harm, then it is permissible to abort it. But aborting it at this stage for fear of difficulty in bringing up children or in providing for them or teaching them, or fear for their future, or because the couple feel that they have enough children – this is not permitted.
3 – It is not permissible to abort the pregnancy once it has become an ‘alaqah (clot) or mudghah (chewed lump of flesh) [i.e., after 40 days’ gestation] unless a trustworthy medical committee has stated that allowing the pregnancy to continue poses a danger to the health of the mother, such that there is the fear that she will die if the pregnancy continues. In this case it is permissible to abort the pregnancy, after exhausting all other means of trying to ward off that danger. 
After the third stage, and after the completion of four months of pregnancy, it is not permissible for you to abort the pregnancy unless a group of trustworthy specialist doctors decide that leaving the foetus in his mother’s womb will lead to the death of the mother; this is after exhausting all possible means of keeping the foetus alive. Performing an abortion subject to these conditions is permitted in order to ward off the greater of the two harms, and to preserve the greater of the two interests.” 
(Quoted from al-Fataawa al-Jaami’ah, vol. 3, p. 1055) 
We ask Allaah to keep us safe and sound and to accept our repentance. May Allaah bless our prophet Muhammad.